Cross-relaxation Rate Constants Research Articles

Modular 31 P wideband inversion transfer for integrative analysis of adenosine triphosphate metabolism, T1 relaxation and molecular dynamics in skeletal muscle at 7T.

For efficient and integrative analysis of de novo adenosine triphosphate (ATP) synthesis, creatine-kinase-mediated ATP synthesis, T1 relaxation time, and ATP molecular motion dynamics in human skeletal muscle at rest. Four inversion-transfer modules differing in center inversion frequency were combined to generate amplified magnetization transfer (MT) effects in targeted MT pathways, including Pi ↔ γ-ATP, PCr ↔ γ-ATP, and 31 Pγ(α)ATP ↔ 31 PβATP . MT effects from both forward and reverse exchange kinetic pathways were acquired to reduce potential bias and confounding factors in integrated data analysis. Kinetic data collected using 4 wideband inversion modules (8 minutes each) yielded the forward exchange rate constants, kPCr→γATP = 0.31 ± 0.05 s-1 and kPi→γATP = 0.064 ± 0.012 s-1 , and the reverse exchange rate constants, kγATP→Pi = 0.034 ± 0.006 s-1 and kγATP→PCr = 1.37 ± 0.22 s-1 , respectively. The cross-relaxation rate constant, σγ(α) ↔ βATP was -0.20 ± 0.03 s-1 , corresponding to ATP rotational correlation time τc of 0.8 ± 0.1 × 10-7 seconds. The intrinsic T1 relaxation times were Pi (9.2 ± 1.4 seconds), PCr (6.2 ± 0.4 seconds), γ-ATP (1.8 ± 0.1 seconds), α-ATP (1.4 ± 0.1 seconds), and β-ATP (1.1 ± 0.1 seconds). Muscle ATP T1 values were found to be significantly longer than those previously measured in the brain using a similar method. A combination of multiple inversion transfer modules provides a comprehensive and integrated analysis of ATP metabolism and molecular motion dynamics. This relatively fast technique could be potentially useful for studying metabolic disorders in skeletal muscle.

Propofol inhibits the voltage-gated sodium channel NaChBac at multiple sites.

Voltage-gated sodium (NaV) channels are important targets of general anesthetics, including the intravenous anesthetic propofol. Electrophysiology studies on the prokaryotic NaV channel NaChBac have demonstrated that propofol promotes channel activation and accelerates activation-coupled inactivation, but the molecular mechanisms of these effects are unclear. Here, guided by computational docking and molecular dynamics simulations, we predict several propofol-binding sites in NaChBac. We then strategically place small fluorinated probes at these putative binding sites and experimentally quantify the interaction strengths with a fluorinated propofol analogue, 4-fluoropropofol. In vitro and in vivo measurements show that 4-fluoropropofol and propofol have similar effects on NaChBac function and nearly identical anesthetizing effects on tadpole mobility. Using quantitative analysis by 19F-NMR saturation transfer difference spectroscopy, we reveal strong intermolecular cross-relaxation rate constants between 4-fluoropropofol and four different regions of NaChBac, including the activation gate and selectivity filter in the pore, the voltage sensing domain, and the S4-S5 linker. Unlike volatile anesthetics, 4-fluoropropofol does not bind to the extracellular interface of the pore domain. Collectively, our results show that propofol inhibits NaChBac at multiple sites, likely with distinct modes of action. This study provides a molecular basis for understanding the net inhibitory action of propofol on NaV channels.

Extending the Applicability of Exact Nuclear Overhauser Enhancements to Large Proteins and RNA.

Distance-dependent nuclear Overhauser enhancements (NOEs) are one of the most popular and important experimental restraints for calculating NMR structures. Despite this, they are mostly employed as semiquantitative upper distance bounds, and this discards the wealth of information that is encoded in the cross-relaxation rate constant. Information that is lost includes exact distances between protons and dynamics that occur on the sub-millisecond timescale. Our recently introduced exact measurement of the NOE (eNOE) requires little additional experimental effort relative to other NMR observables. So far, we have used eNOEs to calculate multistate ensembles of proteins up to approximately 150 residues. Here, we briefly revisit eNOE methodology and present two new directions for the use of eNOEs: applications to large proteins and RNA.

ENORA2 Exact NOE Analysis Program.

We have recently developed an NMR protocol to extract exact distances between nuclei in proteins from an exact interpretation of NOESY buildup intensities (eNOEs). This enabled us to calculate multistate structural ensembles that exhibit realistic spatial sampling and long-range correlations. Our initial studies were laborious and required a deep understanding of the underlying spin dynamics. Here, we present a MatLab package that integrates all data processing steps required to convert intensities of assigned peaks in NOESY series into upper and lower distance limits for structure calculation. Those steps include organization of the data in object format, extraction of autorelaxation and cross-relaxation rate constants by fitting of diagonal peak decays and cross peak buildups, validation of the data, correction for spin diffusion, graphical display of the results, and generation of distance limits in CYANA compatible format. The analysis may be carried out using a full relaxation matrix or a simplified "divide and conquer" approach that allows for partial deuteration of protons. As the program does not require expertise beyond that of standard resonance assignment/structure calculation, it is suitable for experts and nonexperts alike.

Multiple Mechanisms of Propofol Inhibition of the Voltage-Gated Sodium Channel Nachbac: A 19F NMR Investigation

Voltage-gated sodium channels are important molecular targets for anesthetics. The intravenous general anesthetic propofol was found to inhibit NaChBac, a prokaryotic sodium channel from Bacillus halodurans, but little is known about where propofol binds and how propofol binding inhibits the function of this channel. Here, we used 19F-NMR saturation transfer difference (STD) spectroscopy to quantify propofol interactions with NaChBac and to understand the inhibitory mechanisms by propofol. 19F probes were introduced, one at a time, by tagging 1,1,1-trifluoro-3-bromo acetone to site-directed single cysteine mutations that had been computationally predicted to be involved in propofol binding. Quantitative 19F-NMR STD between the 19F probes and 4-fluoropropofol, a fluorinated propofol analog show that propofol binds with different affinities to the sites in different regions of NaChBac. The order of fluoropropofol binding strength, reflected in the cross relaxation rate constant (σ), from the strongest to the weakest, is as follows: the channel activation gate at the cytoplasmic end of the pore, the voltage sensing domain near the gating charge-carrying residues, the ion selectivity filter at the end of the P1 loop, the S4-S5 linker, and the central cavity of the pore. No STD was detectable in the extracellular interface of channel. The finding of multiple binding sites is consistent with the previous observations with the volatile anesthetics isoflurane and sevoflurane. Our results suggest that propofol inhibits NaChBac through multiple sites with distinct mechanisms. As a channel blocker, propofol interferes with the activation gate and selectivity filter and obstructs conductance by binding to the inner pore. As an inhibitory modulator, propofol binding interrupts charge movement in the voltage-sensing domain and restricts the pivot motion of the S4-S5 linker. The study provides a molecular basis for the understanding of propofol inhibitory action on voltage-gated sodium channels. This research was supported by grants from the NIH.

High-resolution three-dimensional macromolecular proton fraction mapping for quantitative neuroanatomical imaging of the rodent brain in ultra-high magnetic fields

A well-known problem in ultra-high-field MRI is generation of high-resolution three-dimensional images for detailed characterization of white and gray matter anatomical structures. T1-weighted imaging traditionally used for this purpose suffers from the loss of contrast between white and gray matter with an increase of magnetic field strength. Macromolecular proton fraction (MPF) mapping is a new method potentially capable to mitigate this problem due to strong myelin-based contrast and independence of this parameter of field strength. MPF is a key parameter determining the magnetization transfer effect in tissues and defined within the two-pool model as a relative amount of macromolecular protons involved into magnetization exchange with water protons. The objectives of this study were to characterize the two-pool model parameters in brain tissues in ultra-high magnetic fields and introduce fast high-field 3D MPF mapping as both anatomical and quantitative neuroimaging modality for small animal applications. In vivo imaging data were obtained from four adult male rats using an 11.7T animal MRI scanner. Comprehensive comparison of brain tissue contrast was performed for standard R1 and T2 maps and reconstructed from Z-spectroscopic images two-pool model parameter maps including MPF, cross-relaxation rate constant, and T2 of pools. Additionally, high-resolution whole-brain 3D MPF maps were obtained with isotropic 170µm voxel size using the single-point synthetic-reference method. MPF maps showed 3-6-fold increase in contrast between white and gray matter compared to other parameters. MPF measurements by the single-point synthetic reference method were in excellent agreement with the Z-spectroscopic method. MPF values in rat brain structures at 11.7T were similar to those at lower field strengths, thus confirming field independence of MPF. 3D MPF mapping provides a useful tool for neuroimaging in ultra-high magnetic fields enabling both quantitative tissue characterization based on the myelin content and high-resolution neuroanatomical visualization with high contrast between white and gray matter.

Interaction of naphthalene derivatives with lipids in membranes studied by the 1H-nuclear Overhauser effect and molecular dynamics simulation

The location, orientation, and dynamics of hydrophobic small molecules in lipid membranes are studied through combined use of solution-state (1)H-NMR and MD simulation. 1-Naphthol and 1-methylnaphthalene were adopted as the small molecules with or without hydrophilic groups. The nuclear Overhauser effect (NOE) measurement was performed for large unilamellar vesicles (100 nm in diameter) composed of dimyristoylphosphatidylcholine (DMPC) and the naphthalene derivative. The transient NOE-SE (spin-echo) scheme previously reported (J. Phys. Chem. B, 2011, 115, 9106-9115) was employed to quantitatively determine the NOE cross relaxation rate constant between DMPC and the naphthalene derivative. The observed NOE shows that both the naphthalene derivatives distribute over a wide domain across the normal of the essentially planar membrane ranging from the hydrophobic core to the hydrophilic headgroup. The experimental NOE information was further refined in combination with the analysis of time correlation functions in MD simulation. It was found that 1-naphthol exhibits a slight preference for pointing its OH group toward the hydrophilic domain of the membrane and that no definite preference can be concluded for the orientation of 1-methylnaphthalene. When 1-naphthol and 1-methylnaphthalene are compared, the NOE is stronger for 1-naphthol due to the restricted motion of the OH group. The slowdown of the 1-naphthol motion is also evidenced by the (1)H spectral line width.

Cross-relaxation imaging reveals detailed anatomy of white matter fiber tracts in the human brain

Cross-relaxation imaging is a new quantitative MRI modality, which allows mapping of fundamental parameters determining the magnetization transfer (MT) effect in tissues, cross-relaxation rate constant ( k) and bound pool fraction ( f). This study introduces a new time-efficient technique for cross-relaxation imaging, which obtains three-dimensional (3D) whole-brain k and f maps with scan time of <30 min and isotropic spatial resolution of 1.4 mm. The technical principle of the method is based on four-point fit of a matrix model of pulsed MT to imaging data obtained with variable offset frequency saturation while using a complimentary R 1 (=1 / T 1) map. Anatomical correlations of in vivo cross-relaxation parametric maps were evaluated in three healthy subjects. The f maps revealed correspondence of areas with highly elevated f = 12–15% to major fiber tracts such as corpus callosum, anterior commissure, optic radiations, and major brain fasciculi. The rest of white matter (WM) demonstrated lower f = 9–11%, resulting in clear visual contrast of fiber tracts. Even lower f = 6.5–8.5% were found in gray matter (GM) with the highest f = 8.5% in the anterior thalamus. Distribution of k was relatively uniform in WM and produced sharp contrast between GM and WM ( k = 1.6 and 3.3 s −1, respectively). The most marked feature of k maps was their ability to visualize the corticospinal tract, which had elevated k = 3.4–3.8 s −1 but appeared invisible on f maps. The observed patterns on f maps can be explained by variations in the density of myelinated fibers, while the trends of k may reflect regional differences in axonal organization. Cross-relaxation imaging can be used in various clinical studies focused on brain development and white matter diseases.

Separation of cross-relaxation and exchange in two-site spin systems with weak spin-spin couplings

A ratio relating the cross-relaxation rates, rate constants, and cross-peak and diagonal peak integrals is used for the analysis of exchanging two-site spin systems with weak scalar spin-spin couplings to extract the rate constants and cross-relaxation rates contributing to the same cross-peaks in two-dimensional nuclear Overhauser enhancement spectra (2-D NOESY). The method to separate contributions from cross-relaxation and chemical exchange into the cross-peaks in NOESY spectra was applied to investigate the intramolecular dynamics of trisulfide 4H, 8H-naphtho[1,8-ef]1,2,3-trithiocine in solutions.

Pulsed Z-spectroscopic imaging of cross-relaxation parameters in tissues for human MRI: theory and clinical applications.

A new method of pulsed Z-spectroscopic imaging is proposed for in vivo visualization and quantification of the parameters describing cross-relaxation between protons with liquid-like and solid-like relaxation properties in tissues. The method is based on analysis of the magnetization transfer (MT) effect as a function of the offset frequency and amplitude of a pulsed off- resonance saturation incorporated in a spoiled gradient-echo MRI pulse sequence. The theoretical concept of the method relies on an approximated analytical model of pulsed MT that provides a simple three-parameter equation for a pulsed steady-state Z-spectrum taken far from resonance. Using this model, the parametric images of cross-relaxation rate constant, content, and T(2) of the semisolid proton fraction can be reconstructed from a series of MT-weighted images and a coregistered T(1) map. The method was implemented on a 0.5 T clinical MRI scanner, and it provided high-quality 3D parametric maps within an acceptable scanning time. The estimates of cross-relaxation parameters in brain tissues were shown to be quantitatively consistent with the literature data. Clinical examples of the parametric images of human brain pathologies (multiple sclerosis and glioma) demonstrated high tissue contrast and clear visualization of the lesions.

Variable Temperature Study of the Cross-Relaxation Dynamics in the Hyperpolarized Xenon-Induced Enhancement of Surface Nuclei

The cross-relaxation rate constants for a three spin system involving hyperpolarized 129Xe, 13C, and 1H nuclei have been determined over a wide temperature range (136−216 K) through observation of ...

Experimental Control of Spin Diffusion in Liquid State NMR: A Comparison of Methods

In this paper, we use the formalism of the first directional derivative of the matrix exponential, to analyze and compare several experimental schemes designed to measure cross-relaxation rate constants between two spins, without having to calculate the effects due to spin diffusion.

Distinctly Different Interactions of Anesthetic and Nonimmobilizer with Transmembrane Channel Peptides

Although it plays no clinical role in general anesthesia, gramicidin A, a transmembrane channel peptide, provides an excellent model for studying the specific interaction between volatile anesthetics and membrane proteins at the molecular level. We show here that a pair of structurally similar volatile anesthetic and nonimmobilizer (nonanesthetic), 1-chloro-1,2,2-trifluorocyclobutane (F3) and 1,2-dichlorohexafluorocyclobutane (F6), respectively, interacts differently with the transmembrane peptide. With 400 μM gramicidin A in a vesicle suspension of 60 mM phosphatidylcholine-phosphatidylglycerol (PC/PG), the intermolecular cross-relaxation rate constants between 19F of F3 and 1H in the chemical shift regions for the indole and backbone amide protons were 0.0106 ± 0.0007 ( n = 12) and 0.0105 ± 0.0014 ( n = 8) s −1, respectively. No cross-relaxation was measurable between 19F of F6 and protons in these regions. Sodium transport study showed that with 75 μM gramicidin A in a vesicle suspension of 66 mM PC/PG, F3 increased the 23Na apparent efflux rate constant from 149.7 ± 7.2 of control ( n = 3) to 191.7 ± 12.2 s −1 ( n = 3), and the apparent influx rate constant from 182.1 ± 15.4 to 222.8 ± 21.7 s −1 ( n = 3). In contrast, F6 had no effects on either influx or efflux rate. It is concluded that the ability of general anesthetics to interact with amphipathic residues near the peptide-lipid-water interface and the inability of nonimmobilizer to do the same may represent some characteristics of anesthetic-protein interaction that are of importance to general anesthesia.

Full matrix Analysis of Cross-relaxation Fails in Fractionally Deuterated Molecules.

We have analyzed cross-relaxation in fractionally deuterated molecules and showed that the full matrix analysis fails except when the dilution is extreme. This is because the isotopic dilution alters the matrix exponential relationship between the observed spectrum and the cross-relaxation rate constants sought. Consequently, an average of the spectra of various isotopomers differs from the matrix exponential of an average relaxation matrix. We have derived a series expansion that allows the determination of the cross-relaxation rate constants in arbitrarily deuterated molecules.

Conformation of the trypanocidal pharmaceutical suramin in its free and bound forms: transferred nuclear overhauser studies.

Suramin is a lead compound for treatment of cancer, HIV, and trypanosomiasis. The conformations of suramin in its free form and bound to phosphoglycerate kinases from T. brucei and S. cerevisae, have been studied in aqueous solutions using nuclear Overhauser effect (NOE) and transferred NOE NMR spectroscopies. The NOE data of the free drug can be accommodated by a model in which many of the single bonds of suramin are unrestricted at room temperature, consistent with molecular mechanics calculations. The angle between the naphthalene ring and the adjoining amide is essentially locked by a strong amide-sulfonate hydrogen bond into one preferred conformation. Another degree of freedom near the termini of the molecule has a rather pronounced preference, and a third exhibits a nearly perpendicular arrangement between the amide and adjacent aromatic ring. The other two degrees of freedom have weaker preferences. Molecular mechanics calculations using AMBER force field and charges on amides and sulfonates obtained from semiempirical or ab initio calculations reproduced the extent of nonplanarity but not the detailed preferences. 13C spin-lattice relaxation, proton NOE, and light-scattering measurements for free suramin indicate that the correlation time of the molecule is approximately 3 ns at 5 mM concentration, suggesting that suramin is multimeric. Lowering the temperature to 5 degrees C causes a dramatic broadening of all of the resonances in the NMR spectra of 5 mM suramin. This broadening probably is associated with further aggregation into micelles. Suramin is monomeric at 0.5 mM and room temperature, and the NOE cross-relaxation rate constants are close to the cancellation condition for a 500 MHz proton frequency; this concentration is typical of blood serum concentrations when the drug is utilized in humans. Changes in the conformational preferences for terminal degrees of freedom are observed in the bound states of suramin based upon the transferred NOE data. The data for the bound state cannot be accommodated by a symmetric conformer. Analysis of the transferred NOESY buildup curves indicates complex kinetics of binding, probably involving an electrostatically bound encounter complex. Despite the weak binding constant, the buildup curves cannot be treated as population-weighted averages of the free and bound cross-relaxation rates, and therefore complete relaxation-exchange matrix analysis has been performed to simulate the data sets.

Least-Squares Method for Quantitative Determination of Chemical Exchange and Cross-Relaxation Rate Constants from a Series of Two-Dimensional Exchange NMR Spectra

We present a new method, the least-error matrix analysis (LEMA), to quantify the dynamic matrix from a series of 2D NMR exchange spectra. The method is based on a weighted averaging of individual d...

Quantitative Determination of Cross-Relaxation Rates in NMR Using Selective Pulses to Inhibit Spin Diffusion

Overhauser effects and hence internuclear distances can be measured accurately with selective experiments designed to suppress spin diffusion. It is essential to consider effects of both transverse and longitudinal relaxationduringselective radiofrequency pulses. Fitting procedures allow one to refine selected cross-relaxation rate constants, and hence determine internuclear distances with improved accuracy. For the sake of illustration, selected cross-relaxation rates are determined that correspond to short- and long-range distances involving two diastereotopic sugar protons in a double-stranded B-DNA dodecamer. Such distances are difficult to distinguish by traditional Overhauser methods because of spin-diffusion effects.

19F-{ 1H} Nuclear Overhauser Effect and Proton Decoupling of 5-Fluorouracil and α-Fluoro-β-Alanine

19F-{ 1H} magnetic double-resonance experiments were performed on model solutions of the antitumor drug 5-fluorouracil (5-FU) and of α-fluoro-β-alanine (FBAL) in order to improve 19F NMR sensitivity for the application in pharmacokinetic studies in vivo. Upon driving the proton spins into saturation, a fluorine signal enhancement (nuclear Overhauser effect) was observed on the order of the theoretical NOE maximum γ H/2γ F, = 53% for purely dipolar coupled 19F- 1H spin systems in extreme narrowing. The dependence of the effect on proton excitation frequency and temporal parameters was measured and cross-relaxation rate constants of 0.07 s −1 (5-FU) and 0.19 s −1 (FBAL) were determined. Irradiation of the proton spin system by a broad pulse during the 19F signal detection period removed FBAL multiplet splittings completely and narrowed the linewidth of this resonance band by a factor of six, Application of proton presaturation in the 19F NMR examination of a patient undergoing 5-FU chemotherapy enhanced the signal-to-noise ratio of the major 5-FU catabolite FBAL detected noninvasively in the liver.

NMR Cross-relaxation Investigated by Molecular Dynamics Simulation: A Case Study of Ubiquitin in Solution

A one nanosecond molecular dynamics simulation of ubiquitin in solution gas been used for the calculation of the total dipolar, the radial and the reorientational correlation functions of 174 interproton NOEs and the 76 peptide chain NH vectors. The NOEs have been classified according to the structural elements they are associated with. Using multiexponential fits of the raw data spectral densities and cross-relaxation rate constants have been determined. Statistical distributions of correlation function parameters are given.On the basis of these data the assumptions underlying the standard method for distance measurement using NOE enhancements have been scrutinized. The separability of elongation and reorientation is verified for the vast majority of NOEs, but the rigid-body assumption is not supported by the simulation results. Relying on a spectral density expression that neither makes use of the product approximation not neglects spatially restricted motion, a "bias-free" (with regard to molecular motion) distance measurement method is suggested and compared with the standard method. Errors in distances up to 24% and 50% occur due to the neglect of the dispersion of order parameters and correlation times, respectively. The preconditions for a class-specific calibration method have been investigated.Within the framework of the product approximation a method for decomposing the total cross-relaxation rate constant into contribution from radial and angular motion has been developed and applied. In several cases distance fluctuation contributes significantly to cross-relaxation with both amplitude and time behaviour.

Polarization-Operator Formalism Description of the Off-Resonance ROSEY Experiment

Polarization-operator formalism was used to describe the behavior of spin- 1 2 homonuclear off-resonance spin-lock effects occurring in the ROESY experiment. The weak-collision case was assumed. Direct- and cross-relaxation rate constants representing T off 1ρ- and T off 2ρ-relaxation processes were evaluated. Off-resonance effects associated with the ROESY experiment were accommodated in the formalism by the inclusion of T off 1ρ relaxation. ROE contributions dominate the cross-relaxation rate when the tilt angle (β) of the effective field (relative to the static B 0 field) in the rotating frame approaches 90°, whereas when β becomes small, NOE contributions predominate. Consequently, a continuous change in the tilt angle of the effective field from 90° to 0° results in a smooth spectral change characteristic of a ROESY to NOESY transition and may be implemented experimentally by the O-ROESY pulse sequence [K. Kuwata and T. Schleich, J. Magn. Reson. A 111, 43 (1994)]. Applications of the formalism include the analysis of off-resonance spin-lock effects arising in the O-ROESY experiment, namely, the dependence of cross-peak intensity on RF offset frequency, thereby enabling assessment of macromolecular motional parameters and internuclear separation distance from the cross-peak intensity dispersion behavior. Simplified expressions for the cross- and direct-relaxation rate constants in the rotating frame were derived from the exact formalism using the approximation ω eτ c ⪡ 1, which provided virtually identical numerical results to those of the exact formalism. For the case of interacting spin- 1 2 nuclei with similar chemical-shift values, the formalism demonstrates, in accordance with other studies, that particular tilt angles of the effective field may be selected to enable suppression of cross relaxation (β = 35.3°) for slowly reorienting macromolecules, or the constraining of the direct- to cross-relaxation-rate-constant ratio to 0.5 at all values of ω eτ c (β = 54.7°). However, at relatively large values of the chemical-shift difference between the interacting spins, these rules do not rigorously apply. Analogous behavior was observed for simulations of the normalized cross-peak intensity vs off-resonance irradiation frequency.